INFERENCE UNCERTAINTY: CHAMBERLIN'S FIRST BALANCED SECTION, WHAT WENT WRONG AND WHY It MATTERS

One hundred years ago R.T. Chamberlin published what is probably the first balanced cross section in history. His section crosses the central Pennsylvania fold-thrust belt and the balancing was done using the excess-area method. The predicted lower detachment is V-shaped and far too deep. The unstated assumptions responsible for the discrepancy remain as problems today for both error analysis and orogenic shortening calculations. The two most critical assumptions are constant bed length-thickness and the presence or absence of displacement on an upper detachment. To examine the importance of these and other assumptions in a modern context, a recent section across the same area by Faill and Nickelsen (F&N, 1999) is evaluated with the area-depth-strain technique. This method uses for control the excess areas of two key horizons and the locations of the detachments; total shortening and layer-parallel strain (LPS) are predicted without assuming constant bed length. Whereas constant bed-length restoration of the F&N section indicates a total shortening of 48.6 mi (78 km) with 24.8 mi (40km) of displacement on an upper detachment in the mid- to upper-Ordovician shale, area-depth-strain analysis shows the result to be very sensitive to whether or not an upper detachment is present and the exact positions chosen for the upper and lower detachments. Assuming the F&N section is conceptually correct, small changes in assumptions (inference uncertainty) allow the total shortening to range from 30 to 87 mi (48-140 km) and displacement on the upper detachment to range from 0 to 57 mi (0-92 km). The preferred approximation has 49.3 mi (79 km) displacement on the lower detachment, little displacement on an Ordovician upper detachment, and LPS of –24% in the base-Silurian marker. The results demonstrate that orogenic shortening values derived from constructed cross sections may have large inference-uncertainty errors.